1. Field of the Invention
The present invention relates to the filtration of signals. More specifically, the present invention relates to a method and an apparatus for digital filtration of signals.
2. The Prior Art
Filtration of signals is used in a variety of different applications. Filters work by responding differently to signals of different frequency. FIG. 1 depicts an example of a signal graphed by magnitude and frequency. This wave is then altered in some way by a filter. Different filters perform different operations on the wave.
FIGS. 2A-2C depict examples of the effects of different filters on the wave in FIG. 1. A common type of filter is one which changes the shape of a wave. An example of the effect of such a filter is depicted in FIG. 2A. Filters can be designed to alter the shape of waves in many different ways. Another common type of filter is a rejection filter, where a portion or portions of the signal is disregarded in favor of another portion. This usually takes the form of rejection based on frequency. An example of the effect of this type of filter is depicted in FIG. 2B. As one can see, the portions of the signal below frequency a and above frequency b have been reduced to zero magnitude, while the portion of the signal between frequencies a and b has been left unchanged.
Another type of filter commonly used is known as a lowpass filter. A lowpass filter filters out portions of the signal with higher than a specific frequency, only allowing the portions of the signal below that specific frequency to pass (hence the name lowpass). An example of the effect of such a filter is depicted in FIG. 2C. As one can see, the portion of the signal above frequency a has been rejected, while the portion under frequency a has been allowed to pass. These are just a few of the many different types of filters known in the prior art.
Variable bandwidth systems are those in which certain information is contained in blocks of frequency (or channels) which have different bandwidths. The simplest way to think of these systems is as a television broadcast system. FIG. 3 depicts a television broadcast system in which all of the channels have the same bandwidth capacity. This is known as a fixed bandwidth system. FIG. 4 depicts a television broadcast system in which the channels may have different bandwidths. This is known as a variable bandwidth system. The advantage of a variable bandwidth system is that it provides more flexibility in setting up the system. In the specific example of television broadcasting, a system could be set up where certain channels have higher bandwidth (allowing for more information) while other channels have lower bandwidths. The channels with higher bandwidth could be used to transmit stations that contain a lot of information (such as movie channels, where picture and sound quality should be the best). The channels with lower bandwidth could be used to transmit stations that contain less information (such as news channels, or audio only channels, where picture and/or sound quality need not be of the highest quality).
A problem arises, however, in filtering signals in variable bandwidth systems. Most prior art filters are hardwired to filter a certain way. Therefore, most individual prior art filters can only handle fixed bandwidth systems. A variable bandwidth filter can be constructed for a fixed data rate system (a system where the input rate of data never can be changed) by having a construction where it is possible to alter the sampling frequency of the input signal, which in turn would alter the bandwidth of the filter. However, the problem with this is that one cannot lower the sampling frequency below the Nyquist rate (twice the Nyquist frequency, which is the highest input signal frequency) because when the sampling frequency falls below the Nyquist rate, aliasing occurs. Aliasing results in frequencies greater than one-half the sampling rate becoming indistinguishable from frequencies in the fundamental bandwidth (between DC and one-half the sampling rate). Thus, for systems with low bandwidths, which can be quite common, it is necessary to use a plurality of filters to perform the task of one filter.
For example, in a variable bandwidth system with a low data rate where the possible bandwidth sizes are 1 MHz, 2 MHz, and 3 MHz, if one wanted to set up a lowpass filter for the incoming signal, one would have to actually have 3 lowpass filters, one for 1 MHz bandwidths, one for 2 MHz bandwidths, and one for 3 MHz bandwidths. This increase in complexity takes up extra space in a system as well as costs extra money.
What is needed is a way to implement a wide range of filters with one single structure, which is capable of performing filtering in systems with low bandwidths and has the flexibility to work under varying sampling frequencies.